High Resolution Study of Deuterated Hydrogen Sulfide in the Region 2400-3000 cm

High resolution Fourier transform spectra of deuterated hydrogen sulfide have been recorded in the region 2400-3000 cm⁻¹. Rotational structures of the ν₁ + ν₂, ν₂ + ν₃ bands of D₂³²S, of the ν₃ and ν₁ + ν₂ bands of HD³²S, and of the ν₁ + ν₂ band of HD³⁴S were analyzed. Band centers and rotational, centrifugal distortion, and resonance parameters were obtained, which reproduce the initial values of the upper energy levels within a mean accuracy of 1.39 × 10⁻⁴ cm⁻¹ for the states (110) and (011) of D₂³²S, 1.61 × 10⁻⁴ cm⁻¹ and 1.82 × 10⁻⁴ cm⁻¹ for the states (001) and (110) of HD³²S, and 2.09 × 10⁻⁴ cm⁻¹ for the state (110) of HD³⁴S, respectively.     

The central limit problem for convex bodies

It is shown that every symmetric convex body which satisfies a kind of weak law of large numbers has the property that almost all its marginal distributions are approximately Gaussian. Several quite broad classes of bodies are shown to satisfy the condition.

     

Synthesis and characterization of 1,2-cyclohexanedione bis-benzoyl-hydrazone and its application to the determination of ti in minerals and rocks

The synthesis, spectroscopic characteristics and analytical applications of 1,2-cyclo-hexanedione bis-benzoylhydrazone are reported. The reaction of this new compound with titanium(IV) has been studied spectrophotomelrically. An orange 1:2 metal/ligand complex (lambda(max)= 477 nm, = 1.05 x 10(4) l.mole(-1).cm(-1)) is formed at pH 1.75-3.0 in 3:2 v v ethanol-water medium. The method is simple and selective and has been satisfactorily applied to the determination of titanium in bauxite, Portland cement, amphibolites and granites.     

Asymptotic expansions for the truncation error in Ramanujan-type series

The Ramanujan Journal - Many of the fastest known algorithms to compute $$\pi $$ involve generalized hypergeometric series, such as the Ramanujan–Sato series. In this paper, we investigate...     

On the verification of the applicability of the orthotropic plate wave theory to paper

In the literature one basic work can be found that describes an attempt to verify the applicability of the orthotropic plate wave theory to paper. In the present study we have repeated the key experiment and also modified the original experimental set-up to be able to make new complementary measurements. The performed verification attempt is based on a key experiment in which an ultrasonic resonance method is used. When it is applied to paper, a second resonance can be observed in addition to the one that originates from the asymmetric A0 mode. The result of the verification experiment is conclusive only if the source of this second resonance is the symmetric S0 mode. Our results show that the second resonance is not generated by the S0 mode. Instead, they indicate that the source is a longitudinal wave propagating in the thickness direction of the paper. We therefore conclude that the applicability of the orthotropic plate wave theory to paper cannot be verified by performing the key experiment that is described in the literature.     

Radiation enhanced outdiffusion during ion implantation

For a systematic prediction of the radiation-enhanced outdiffusion occurring during implantation, the use of a model based on the effect of vacancy flow on diffusion is described. The model agrees reasonably well with experiments in all twentysix measured cases. For the systematic understanding of the radiation enhanced outdiffusion, an approximative diagram based on the activation energy of self-diffusion is constructed for all pure elements and its application possibilities are discussed.     

High-Resolution Infrared Spectrum of CD(3)CN: Analysis of the Interacting nu(3) and nu(6) Bands and Evaluation of the A(0) Constant

The infrared spectrum in the range 900-1230 cm(-1) including the fundamental bands nu(3) and nu(6) of CD(3)CN has been studied. The resolution attained was 0.0025 cm(-1) in the measurement on the Bruker 120 HR Fourier spectrometer in Oulu. About 4000 lines were assigned in the nu(6) band. For the weak nu(3) band, which has not been observed earlier directly, we were able to assign 206 lines in three subbands K=8-10. These lines become detectable due to the strong nu(3)/nu(6) Coriolis resonance. There is also an l(1,-2) resonance between nu(3) and nu(6), which made it possible to obtain a value 2.647721(50) cm(-1) for the axial rotational constant A(0), when D(0)(K) from force field calculations was applied. Different types of resonances with the overtone 3nu(8) and the combinations nu(4)+nu(8) and nu(7)+nu(8) were observed. A fit with a standard deviation of 0.0019 cm(-1) was attained by using a model of 10 different resonances. Copyright 2001 Academic Press.     

Weak solutions for a system of nonlinear Klein-Gordon equations

Summary We prove the existence and uniqueness of weak solutions of the mixed problem for a class of systems of nonlinear Klein-Gordon equations. Uniqueness is proved when the spatial dimension is either n=1, 2or 3.Partially supported by CNPq-Brasil.     

The boundary element spline collocation for nonuniform meshes on the torus

The spline collocation method for a class of biperiodic strongly elliptic pseudodifferential operators is considered. As trial functions tensor products of odd degree splines are used and the collocation is imposed at the nodal points of the tensor product mesh. It is shown that the collocation problem is uniquely solvable if the maximum mesh length is small enough. Moreover, the approximation is stable and quasioptimal with respect to a norm depending on the order of the operator and the degree of approximating splines. Some convergence results are given for general and quasiuniform meshes. The results cover for example the single layer and the hypersingular operators.